We find the optimal solutions by a computational scheme based on multi-functional optimization [1]}. In particular, we systematically explore the parameter space using genetic algorithms [2]} to identify feasible values of the observables that are compatible with the constraints and find the Pareto optimal front between \(\eta \) , \(v\)  and \(\Delta \sigma \)  as a function of the free parameters. We employ this method for different numbers of proofreading steps.
